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Chapter 6: Problem 361

In the following exercises, translate and solve. 120\(\%\) of 55\(\quad\) is what number?

Short Answer

Expert verified
66

Step by step solution

01

Convert Percentage to Decimal

First, convert the percentage to a decimal by dividing by 100. Therefore, 120% becomes \( \frac{120}{100} = 1.20 \).
02

Set Up the Equation

Next, set up the equation to find the unknown number. If 120% of 55 is some number (let's call it \( x \)), then \( 1.20 \times 55 = x \).
03

Solve the Equation

Now, multiply 1.20 by 55 to find the value of \( x \). Therefore, \( x = 1.20 \times 55 = 66 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

converting percentages to decimals
When working with percentages, it's often easier to convert them to decimals to simplify calculations. To do this, divide the percentage by 100. This helps us express the percentage as a fraction of one whole. For example, to convert 120% to a decimal, divide 120 by 100, which gives us 1.20. Remember that the % symbol means 'per hundred'.
Here's a quick recap:
  • 120% = 120 / 100 = 1.20
  • 45% = 45 / 100 = 0.45
  • 78% = 78 / 100 = 0.78
Converting percentages to decimals is a crucial first step in many percentage problems, making it easier to perform further calculations.
setting up equations
After converting the percentage to a decimal, the next step in solving a percentage problem is to set up an equation. This equation helps you find the unknown value you're trying to determine. In the example of finding 120% of 55, we start by letting x be the number we're looking for.
Here鈥檚 how to set it up:
  • We know 120% is 1.20 as a decimal.
  • So, 120% of 55 can be written as 1.20 times 55.
  • This gives us the equation: 1.20 脳 55 = x.
In this setup, 1.20 is the multiplier (converted percentage), 55 is the base value, and x is the unknown number. Setting up the equation correctly is essential for finding the correct answer.
multiplication
Once you have your equation set up, it's time to solve it, which usually involves multiplication. Multiplication in this context means scaling the base number by the converted percentage.
Let's multiply 1.20 by 55 as shown in the solution:
  • 1.20 脳 55
  • To do this, you can first compute 1.2 脳 55 (ignoring the extra decimal place for simplicity).
  • This is equivalent to (1.2 脳 50) + (1.2 脳 5), which equals 60 + 6 = 66.
So, multiplying 1.20 by 55 gives us 66. Therefore, 66 is 120% of 55. Always ensure the multiplication is done accurately to get the correct answer. This step is crucial as it brings you to the final solution of your problem.

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